Stefano Bartolini° and Luigi Bonatti°°

THE MOBILIZATION OF HUMAN RESOURCES AS AN EFFECT OF

THE DEPLETION OF ENVIRONMENTAL AND SOCIAL ASSETS

ABSTRACT: In this paper, the growth process is not fed by the accumulation of productive assets

(physical and/or human capital, knowledge…), but by the depletion of environmental or social

resources, which induces individuals to increase their labor supply in order to consume more of the

market goods that substitute for the depleted resources. Hence, production is expanded, thus eroding the

resources’ ability to regenerate, which decreases with aggregate production. Within this context, the

‘green’ net national product is derived and it is shown how a regulatory authority should manage the

resources for achieving Pareto-optimality.

KEY WORDS: Renewable resources, Negative externalities, Market failures, Net national product.

JEL CLASSIFICATION NUMBERS: J22, O41, Q28.

Corresponding author: Luigi Bonatti – via Moscova 58 – 20121 MILANO (Italy); phone:

39+02+6599863; e-mail: Luigi.Bonatti@unibg.it

° Dipartimento di Economia Politica - Università di Siena °° Dipartimento di Scienze Economiche “Hyman P. Minsky” - Università di Bergamo

1

1. INTRODUCTION*

There is an increasing awareness among economists that a better understanding of how time and

“effort” devoted to market activities are determined is crucial for explaining growth and development

processes. This paper intends to contribute to this understanding by presenting a neoclassical model in

which the growth process is not fed by the accumulation of productive assets (physical and/or human

capital, knowledge…), but by the decumulation (depletion) of a commonly owned resource (an

environmental or social asset) that each household can use at no cost. Given that this renewable resource

affects positively individual utility, households react to its depletion by increasing their labor supply in

order to buy more market goods as substitutes for its declining services. By so doing, each of them

stimulates production and contributes to a further deterioration of the resource, since its ability to

regenerate is a negative function of aggregate production. This ignites a cumulative process. However,

this process cannot go on forever: in the absence of capital accumulation or technological progress,

growth in per capita output can be fed only by the increase in the proportion of the households’ time that

is sold on the market in order to raise their purchasing power and to buy increasing amount of

substitutes for the diminishing resource.1 Hence, the economy converges to a steady state, but under

laissez faire this steady state is characterized by an inefficiently low endowment of the commonly

owned resource and by an inefficiently high level of labor effort, market production and consumption of

market goods.

* A special thank to E. Bonatti, A. Leijonhufvud and L. Punzo, who encouraged and discussed these ideas since their

beginning. Thanks for useful comments also to G. Becattini, L. Bosco, E. Cresta, M. Dardi, V. Ferrante, A. Gay, D.

Heymann , F. Luna, L. Marengo, G. Mondello, U. Pagano, R. Palma, M. Pugno, P. L. Sacco, A. Vercelli, G. Wagner.

The usual disclaimer applies.

1 It is straightforward that perpetual growth in per capita output can be generated--as in Solow (1956)--by adding an

exogenous source of technological progress. It should be clear that the objective of the paper is not to propose a self-

sufficient growth theory but rather to model a mechanism that may contribute to explain important aspects of the

growth process, in the awareness that the mobilization of human resources has to be supplemented by other sources of

growth in order to generate perpetual growth.

2

The process described above is open to more than one interpretation. If the resource is

interpreted as an environmental asset, one can think of its deterioration as due to the pollution or over-

exploitation brought about by some market activity, which induces defensive consumption on the part of

the households, thus resulting in a further expansion of private consumption and production.2 According

to a sociological interpretation of the process, the institutional and immaterial bases of communitarian

organizations of life are undermined by the expansion of market activities, thus forcing the individuals

to satisfy their needs by buying and selling goods and services on the marketplace. In other words, the

2 Along these lines, we follow Fred Hirsch, who emphasizes that to a large extent growth in advanced economies is due

to an increase in defensive consumption. Hirsch interprets the notion of defensive consumption in a broad sense,

consistently with the idea that reactions to a situation of general decay may be very general and that individuals can

compensate for deterioration in everything that is public with the wealth and concern for everything that is private.

Among the examples contained in the literature on defensive consumption, one has: medical expenses to treat illnesses

due to environmental deterioration or tranquilizers and sleeping pills, the consumption of which is closely correlated

with noise pollution, soundproofing (double glazing, etc.), anti-pollution expenses, land reclamation, defense against

crime. The demand for package holidays may also be considered sensible to deterioration of the local environment, or

swimming pools can be considered substitutes for water quality deterioration. Typically, agents are able to escape the

deterioration of the environment by deciding, for example, to buy a weekend cottage in pleasant surroundings or more

simply by moving to a more comfortable city house. In any event, the limits of the concept of substitute are largely

contiguous on those of psychological inquiry. What the reactions to psychological malaise and stress may be in terms

of consumption is an open question. The econometric literature on defensive consumption displays a number of

conceptual difficulties--evidenced, for example, by the variety of definitions of defensive expenditure--which derive in

part from a failure to understand that the concept of defensive expenditure is a sub-case of the concept of substituted

good (which is clearly codified). In the set of substitutes it is the sub-set of substitutes for environmental goods (i.e. for

the free goods subject to negative externalities). In the opinion of these authors, however, it is difficult to give plausible

statistical substance to the concept, due to the difficulty of identifying spending for defensive reasons among the items

in the GNP, constructed on other criteria. The strategy followed is generally highly restrictive, in that only classified as

defensive is spending which is certainly and wholly such: spending on environmental purification, on land reclamation,

on pollution-related diseases. The estimates obtained are not negligible, but on the admission of the authors themselves

they are enormously under-estimated.

3

weakening of these institutions enlarges the sphere of market relations; in its turn, this enlargement

causes further erosion of these institutions. As different aspects of this general tendency in advanced

societies, one may include heterogeneous phenomena like the progressive privatization of certain

resources (land, water…) or services (health, transportation… ) that were predominantly provided by

public agencies, the “commodification” of leisure, or the diminishing role of the family as provider of

services (children and elderly care, meals preparation…).

Other implications of our model for an economy under laissez faire are the following:

1) Exogenous technological progress3 making labor more productive increases steady-state labor supply

and production, thus causing a negative impact on the environmental asset. Therefore, technological

advances boosting productivity but with no effect on the incidence of productive activities on the

environmental asset may even lead in the long run to a worsening of the households’ lifetime welfare.

2) In contrast, the use of technologies with a less detrimental impact on the environmental asset leads in

the long run to a lower level of production and consumption of market goods, since the commonly

owned resource will be less depleted and households will be less dependent on market goods in order to

satisfy their needs. As a result, exogenous technological progress reducing the negative incidence of

productive activities on the environmental asset raises the steady-state welfare of the households.

3) Exogenous technological advances improving the ability of produced goods to substitute for the

environmental asset lead in the long run to more production and consumption of market goods. Hence,

the introduction of better substitutes for natural or social assets may worsen the welfare of future

generations. This is at odds with the literature on sustainable development, which implicitly assumes

that a high degree of substitutability between 'man-made' goods and natural resources is welfare

improving for future generations.4 In contrast, our model shows that improving the possibility of

3 In the model, technological progress takes the form of a shift in a parameter entering the production function.

4 In this literature, the degree of substitutability between ‘man-made’ capital and natural capital is considered crucial

for sustainability if the condition for sustainability is that the aggregate stock of capital ('man-made' plus natural)

should not decline ('weak' sustainability) (see, for instance, Hartwick, 1977). In contrast, the degree of substitutability

does not matter if the condition for sustainability is that there should be no net damage to environmental assets ('strong'

sustainability) (see, for instance, Pearce et al., 1990; Daly, 1991).

4

substituting man-made goods for environmental assets can accentuate that self-reinforcing process of

resources’ depletion which may lead to a long-term worsening of individual well-being.

4) An increase in population tends to raise per-capita output. Indeed, everything that exerts greater

pressure on natural (or social) assets and that accelerates their decline induces individuals to react by

relying more on market goods in order to satisfy their needs, thus raising the steady-state level of

economic activity. Hence, the associated steady-state level of households’ welfare will be lower.

Therefore, an implication of the model is that the long-run equilibrium level of per-capita output is

higher as the population and/or the negative impact of production on commonly owned resources

become larger.5 In contrast, policies that reduce population growth and the impact of market activities

on environmental and social assets restrain the steady-state level of per capita output.

The paper is organized as it follows. Sections 2 presents the model; section 3 compares the path

of the economy obtained under laissez faire to the path consistent with the Pareto-optimal plan; section 4

presents a Cobb-Douglas example in order to discuss the steady-state effects of parametric changes;

section 5 concludes.

2. THE MODEL

5 The prediction that an increase in population will raise the steady-state level of per-capita output is consistent with the

predictions made by models of technological change concerning the impact of population increase on the steady-state

rate of growth of the economy. According to Kuznets (1960), higher population density can explain the

disproportionally larger number of innovations in cities, since it boosts technological progress by favoring intellectual

contacts among people and labor specialization. In endogenous growth models (see Grossman and Helpman, 1991;

Aghion and Howitt, 1992; Kremer, 1993), an increase in population spurs technological change and economic growth

by increasing the size of the market, because the cost of inventing a new technology is independent of the number of

people who use it. However, our model has normative implications regarding the desirability of population increases

which are at odds with those stressed by models of endogenous technological change, since our prediction depends on

the increase in negative externalities due to congestion (increased pressure on environmental and social assets), rather

than on positive externalities due to scale effects.

5

We consider an economy in discrete time with an infinite horizon. For simplicity and without

loss of generality, we assume that an equal number of identical households and firms operate in this

economy.

The households

Population is constant. There is a large number J of households who have finite lifetimes: they

have a strictly positive and constant probability , 01, of dying in each period. Thus, the probability

of dying in a certain period is assumed to be independent of the age of the individual; and it is also

assumed that the mortality rate of a large group of households does not fluctuate stochastically even

though each individual's life span is uncertain. This implies that at the end of each period a constant

number J of households dies and is replaced by an equal number of newly born individuals.

The discounted sequence of utilities that the representative household expects during his/her

lifetime is given by

it+i

i=

U ,0

(1-), 01, (1)

where Ut+i is the period utility function, and is a time-preference parameter. The period utility

function of the representative household is increasing in its three arguments:

Ut=U(Xt,C2t,Lt), UX>0, UC>0, UL>0, UXX<0, UC2C2<0, ULL<0, UXC2

=UXL=UC2L=0, (2)

where Xt is the amount of services generated by some consumer activity, C2t is the amount of the single

good produced in the economy that is consumed in t as a basic good, and Lt is leisure. For simplicity

and without loss of generality, the technology adopted by the households to produce the services

positively entering their utility function is assumed to be linear:

Xt=Rt+C1t, 0, (3)

where Rt is the stock of a renewable resource and C1t is the amount of the produced good that is

combined with Rt to produce Xt. Note that also C1t -- as it is the case for C2t -- is used for consumption

purposes. Moreover, there is non-rivalry in the consumers' use of the resource Rt, from which no

consumer can be excluded: it has the nonexclusive nature typical of a resource of common property that

cannot be produced. The parameter may be interpreted either as a strictly technological parameter

prescribing the quantity of a privately appropriable good that is necessary -- given the stock Rt -- to

6

produce the amount of Xt desired by the consumers, or as a measure of the efficiency of C1t as a

substitute in consumption for the resource of common property.

The total time available to each household in every period is normalized to be one. Thus,

Lt=1-Ht, 0Ht1, (4)

where Ht are the units of time spent working in period t by the representative household.

The period budget constraint of the representative household is the following:

C1t+C2tWtHt+t, (5)

where the single produced good is the numéraire of the system (and its price is normalized to be one),

Wt is the wage rate per unit of time, and t is the share of total profits distributed to each household. For

simplicity, we assume that the property rights on firms are evenly distributed as households' initial

endowments: newly born individuals inherit their claims on firms' profits from the households that have

just died. Since both households and firms are identical, we can ignore the possibility that these rights

are traded among agents.

The firms

There is a large number J of perfectly competitive firms. Each of them produces a non-storable

good Yt using only labor:

Yt=Y(NtHt), Y’>0, Y’’<0, (6)

where Nt is the number of workers employed in t by the representative firm.

In each period, the representative firm must choose the combination of Ht and Nt that

maximizes its profits t, which are given by

t=Yt-WtHtNt. (7)

The renewable resource

The resource Rt is subject to a spontaneous flow of renewal but it is damaged by productive

activities:

Rt+1=-JYt+Rt+A, 01, 0<(1-)/J, A0, Rt0, R0 given. (8)

By interpreting Rt as an indicator of the quality in t of some environmental resource that all

households can use at no cost in every period, one can think of firms as freely disposing of their

polluting waste because of the lack of property rights on the resource. Although a single firm's

7

productive activity has a negligible impact on the environmental quality, the aggregate effect of firms'

production in period t on Rt+1 is not negligible and depends on both the number of producers J and the

technological parameter . The waste accumulated during the productive process is disposed of at the

end of the period and damages the environment in the next period. In other words, the negative

externality caused by each single firm is only intertemporal: (8) captures a productive technology whose

negative inpact on the environment is not immediate. According to this interpretation, the level of

economic activity remaining equal, a larger Rt in the present entails better environmental quality in the

future.

Market equilibrium conditions

Since the single good produced in this economy cannot be stored, it can be only consumed.

Thus, equilibrium in the product market implies:

Yt=C1t+C2t. (9a)

For equilibrium in the labor market, one needs:

H = H ,td

ts (9b)

J N = J,td (9c)

since all the households actively participate in the labor market.

3. COMPARISON BETWEEN THE LAISSEZ-FAIRE PATH AND THE PARETO-OPTIMAL

SOLUTION

The trajectory of the economy and the steady state under laissez faire

In the absence of any asset that can be privately accumulated, the decision problem of each

single household is static. Indeed, each single household can ignore the negligible impact of its own

decisions on the future level of Rt. Therefore, considering (1)-(5), one can solve its problem by

maximizing Ut=U(Rt+(WtHt+t-C2t),C2t,1-Ht) with respect to C2t and Ht, thus obtaining the

optimality conditions

UX=UC2 (10a)

and

WtUX=UL. (10b)

8

Solving the maximization problem of the representative firm and using (9), we obtain that along

an equilibrium path

Wt=Y’. (11)

Thus, the optimality conditions (10) evaluated along an equilibrium path can be rewritten as

2t

t2t2ttt

t

t2t2tttC

)H-1,C),C-)H(((R

X

)H-1,C),C-)H(((R

YUYU (12a)

and

t

t2t2ttt

t

t2t2ttt

t

tL

)H-1,C),C-)H(((R

X

)H-1,C),C-)H(((R

H

)H(

YUYU

d

dY . (12b)

Considering (6) and (9), one can rewrite (8) as

Rt+1+JY(Ht)-Rt-A=0. (12c)

The system (12) governs the motion of the economy along an equilibrium path. Note that the

discount factor does not enter the equations governing the equilibrium path of this market economy,

since the households’ decisions have no intertemporal dimension. A steady state can be characterized by

setting Ht=H, C2t=C2 and Rt+1=Rt=R in (12). Therefore, the steady-state stock of Rt is given by

)-1(

(H)J-AR

Y

, (13)

and the steady-state values of Ht and C2t can be found by solving the system

(H,C2)= , (14a)

(H,C2)=, (14b)

where (H,C2)

X

H-1,C,C-H)()-(1J-)-(1

A

C

H-1,C,C-H)()-(1J-)-(1

A

22

2

22

YU

YU

and

(H,C2)

X

H-1,C,C-H)()-(1J-)-(1

A

H

)H(

L

H-1,C,C-H)()-(1J-)-(1

A

22

22

YU

d

dY

YU

.

The trajectory of the economy and the steady state according to the Pareto-optimal solution

9

One can obtain the Pareto-optimal path by solving the problem of a benevolent planner that

maximizes the expected lifetime sequence of discounted utilities of the representative household. Since

the benevolent planner internalizes the negative effects that each productive activity causes on the future

endowment of the renewable resource, its optimization problem is genuinely intertemporal. Thus, one

can derive the conditions that a Pareto-optimal path must satisfy by maximizing

t

t=0

U(Rt+(Y(Ht)-C2t),C2t,1-Ht)-t[Rt+1+JY(Ht)-Rt-A] with respect to Ht, C2t, Rt+1 and t,

where the multiplier t can be interpreted as the (current) shadow price of Rt along a Pareto-optimal

path. Hence, the benevolent planner must satisfy the optimality conditions:

UX=UC2 (15a)

and

Y’UX=UL+JtY’, (15b)

the Euler equation:

UX+t+1=t, (15c)

and the law of motion of the resource given by (12c).

Moreover, it must satisfy the transversality condition:

limt

t

Rtt=0. (16)

By comparing (10b) and (11) with (15b), one can see that--in contrast with individual agents--a

benevolent planner must decide about the allocation of time by taking into account also the impact that a

current increment in work effort will have on the future level of Rt by determining an increase in current

production.

Again, the steady-state level of Rt is given by (13) and the steady-state values of Ht and C2t can

be found by solving the system

(H,C2)= , (17a)

(H,C2)=)-(1

J-

. (17b)

Comparing the steady state obtained under laissez faire to the steady state consistent with the Pareto-

optimal solution

10

The following propositions summarize the differences emerging at steady state between the

laissez-faire equilibrium and the Pareto-optimal solution:

Proposition 1 The steady-state working time is strictly greater under laissez faire than it is following the

Pareto-optimal solution.

Proof: One can check that

0H

C

(.)

2CH 2

d

d. (18)

By comparing (14b) to (17b), it is easy to conclude that (18) entails Proposition 1.

Proposition 2 The steady-state level of productive activity is strictly larger under laissez faire than it is

following the Pareto-optimal solution.

Proof: Since Y’>0, Proposition 2 follows from Proposition 1.

Proposition 3 The steady-state level of the renewable resource is strictly lower under laissez faire than it

is following the Pareto-optimal solution.

Proof: It follows straightforwardly by inspecting (13) and by considering Proposition 2.

The content of Proposition 3, namely that in the long run the depletion of a renewable resource

tends to be more accentuated along a laissez-faire path than along a social-optimum path, is well known

to environmental economists (see e.g. Smulders, 2000). However, their focus is on causality going only

from the expansion of market activities to the erosion of environmental or social assets. In contrast, the

original growth mechanism proposed in this paper takes into account also causation going in the

opposite direction, since the need to substitute for the services provided by declining commons induces

people to rely more heavily on market goods, thus boosting market activities. In other words, differently

than for those economists emphasizing the negative impact that the depletion of some renewable

resource may have on growth, in this paper the erosion of environmental or social assets feeds the

growth process.

Similarly, the contents of Proposition 1 and 2 is common to models formalizing the idea that the

concern for social status is an important motivation driving individual behavior (see Cole et al., 1992;

Fershtman et al., 1996; Corneo and Jeanne, !999): also in this literature, indeed, inefficiently high levels

of working time and output are typically the result of the negative externalities that individuals inflict

11

upon others. However, the policy implications of these models are quite different than the agenda

suggested by our model. If the quest for social status is a pulse that “nature imposes upon us”, as Adam

Smith (1982) claimed in The theory of moral sentiments, there is little that collective action can do for

avoiding the sub-optimal outcome due to the fact that total social reward within a group is fixed and

aggregate satiation is impossible. In contrast, if the externalities are generated by productive activities

that have a negative impact on some environmental or social asset, there is more room for corrective

actions. An example of these corrective actions is proposed in the next paragraph.

The optimal management of the resource and the ‘green’ net national product

Assume that there is a regulatory authority that can charge a price Pt for any unit of Rt+1 that is

depleted because of the production of Yt. As a consequence, the profits of the representative firm are

now given by

t=Yt(1-Pt)-WtHtNt. (19a)

The authority spends what it collects from the firms to pay a subsidy St to each household:

St=YtPt. (19b)

Hence, the representative household’s budget constraint becomes:

C1t+C2tWtHt+t+St. (19c)

Given (19), equation (10b) becomes

Y’(1-Pt)UX =UL. (20a)

If the authority’s objective is to lead the economy along a Pareto-optimal path, it must set Pt so

as to satisfy:

X

tt

JP

U , (20b)

where the motion of t must satisfy the Euler equation (15c) and the transversality condition (16).

Equations (20) – together with (12c), (15a), (15c) and (16) -- characterize a market equilibrium

path that is Pareto-optimal: the intervention of the regulatory authority allows to decentralize the Pareto-

optimal solution.

The gross national product (GNP) is given by Yt=C1t+C2t, and it cannot be considered a

reliable indicator of welfare in period t. Indeed, national accounting can represent an acceptable

12

approximation of the true human well-being at a given point in time only if it takes into account the

value of the net investment in environmental or social asset and the value of all components entering the

individual utility function (inclusive of leisure time and of non-market commodities such as those

services rendered by environmental and social assets). Such an amended indicator is the ‘green’ net

national product in period t, gtNNP . In this regulated economy, such indicator is given by

gtNNP = PtRt+C1t+ C2t+Wt(1-Ht)+Pt[ tt R)-(1-JY-A ], (21)

where in our framework human well-being depends on the ‘consumer commodities’ entering the

households’ utility function, namely Xt=Rt+C1t, C2t and Lt=1-Ht, and the net investment in

environmental or social asset is given by ttt1+t R)-(1-JY-AR-R . Note in (21) that Pt is given

by (20b) and that Wt= (1-Pt)Y’ represents the opportunity cost of time.

4. A COBB-DOUGLAS EXAMPLE: STEADY-STATE EFFECTS OF PARAMETRIC

CHANGES

Let us assume that (2) is specified by

U(Xt,C2t,Lt)=ln(Xt)+ln(C2t)+(1--)ln(Lt), 0, 0, +1, (22a)

and that (6) is specified by

Y(NtHt)=(NtHt), 0<<A/J, 01, (22b)

where is a parameter measuring the state of technology.

The trajectory of the economy and the steady state under laissez faire

Given (22), equations (12) can be rewritten as

,C)CH(+R 2t2ttt

(23a)

t2ttt

1-t

H1

)--1(

)CH(+R

H

(23b)

and

ARHJR tt1+t , (23c)

13

where (23a) and (23b) can be used to derive: Rt=

tt

1-t

t H--1

)H1(H)+(=)(H

R ,6

)--1(

)H-1(H-H=)(HC

t1-

ttt11t

C and .

)--1(

)H-1(H=)(HC

t1-

tt22t

C By using Rt=R(Ht),

one can write (23c) as a difference equation in Ht that governs the evolution of this economy under

laissez faire:

R(Ht+1)= A)H(HJ tt R , (24)

By setting H=Ht+1=Ht in (24), we obtain the equation that any steady state value of Ht must satisfy:

0=AHJH)-1(--1

)H1(H)+Z()-1(=Z)(H,

1-

, (25)

where Z=, 0H1.

One can easily show that there exists only one value of H, H=H*, satisfying (25) (see the

Appendix). By linearizing (24) around H*, we obtain

=H*-H 1+t1

t H*)(JH*)-H(

-1

*HH1+t

1+t

1t

H

)(H

d

dRH*)-(H t , (26)

where H0 is assumed to be in a neighborhood of H*: along the path governed by (26) Ht converges to

H* (see the Appendix).

Steady-state effects of changes in , J and under laissez faire

Technological progress makes labor more productive. Other things remaining equal, firms pay

higher wages, thus increasing the shadow price of time. On the other hand, there is an income effect,

since technological progress makes households feel richer both as workers and as firms' owners, thus

pushing them to enjoy more leisure. However, in this context, the increased productivity tends to boost

production and to reduce the future endowment of the renewable resource, thus inducing the households

to substitute for this reduced endowment by buying more of the produced good. This will stimulate the

households to supply more labor. As a result, at steady state the households devote more time to work:

6 Note that H0=R-1(R0), where R0 is given.

14

H *

07 entailing Y *

0. Given the negative externalities caused by production, an improved state of

technology can even lower the steady-state well-being of the representative household, especially when

the detrimental impact of a higher level of economic activity on the renewable resource is relatively

strong with respect to the efficiency of the produced good as a substitute for the renewable resource:

-1

J is a sufficient condition for having

U *

08. Note that it is more likely that this condition is

fulfilled when the number of firms and households operating in the economy is larger: the presence of a

larger number of private agents exacerbates the aggregate effect on the renewable resource due to

increases in individual market production.

It is worth to emphasize that an increase either in the parameter measuring the incidence of each

firm's level of activity on the renewable resource or in the number of firms and households raises the

steady-state level of per-capita output: H *

J09 entailing

Y *

J0. In other words, technologies that

have a larger impact on Rt generate a higher steady-state level of per-capita output by inducing the

households to work more, so as to finance their increased use of the produced good as a substitute for

the renewable resource that is depleted more intensively. The same effect is caused by an increase in

total population. Therefore, the prediction that a larger population of firms and households gives a

positive contribution to the growth of per-capita output is obtained by the model, but without relying on

7.0

*)()-(1J-)--(1*)()((H*))+)(-1(

*)()-(1J-)--(1H*)-1(*)H()(

*H

1-1-22-

1-

HH

H

8

H*)()-(1J-)-(1

A

H*)()-(1J-)+(

*H

*U*H*U

, where*H-1

)--(1-

H*)()-(1J-)-(1

A

H*)()-(1J-)+(

*H

*U1-

,

which – by taking into account (23b) -- can be written as .0H*)()-(1

J-)-(1A

H*)()-(1J

*H

*U1-

9

H *

J

(1- - ) (1 - )

- )( + ) (H*) (1 - - ) - J(1 - )

-2 -1 -

(

( ( ) ( (.

H*)

H*) H*)10

2 1

15

economies of agglomeration or on the presence of a larger number of agents, each of them producing a

negligible externality in favor of all the others. This increase in the steady-state level of per-capita

output goes together with a decrease in the steady-state level of utility of the representative household:

U *

J010. The higher level of output per head cannot offset the impact on individual welfare of less

leisure and a lower stock of renewable resource.

An increase in the parameter can be interpreted as an improvement of the produced good in its

ability of substituting for the renewable resource. One should expect that this improvement would

induce the agents to work more in order to buy an increased quantity of the improved market good, thus

boosting production. This is actually the case: H *

011 entailing Y *

0.

The trajectory of the economy and the steady state according to the Pareto-optimal solution

Given (22), equations (15) can be rewritten as

,C)CH(+R 2t2ttt

(27a)

t2ttt

1-t

H1

)--1(

)CH(+R

H

+ 1-

tt HJ (27b)

and

)CH(+R 2ttt

+t+1=t. (27c)

The law of motion of the resource is given by (23c), and any steady state value of Ht must

satisfy (25), where now Z=)-(1

J-

. Since

1H

1H0 whenever0

Z

H

0(.)d

d, one can verify

that H*>H°, where H° is the steady state consistent with the Pareto-optimal solution.

10 .0H*)()-(1

J-)-(1A

H*)()-(1)+(

*H

*U

J

*H

J

*U

11

H * H*) - H*) (1- - )

- )( + ) (H*) (1- - ) - J(1 - )

-1

-2 -1 -

( ) ( ( (

( ( ) ( (.

1

10

2 1

H*)

H*) H*)

16

5. CONCLUDING REMARKS

Human resources mobilization has been largely ignored by neoclassical growth modeling. The

reason is that this literature concentrates on other determinants of growth, such as capital accumulation

and technical progress. Symmetrically, the model presented in this paper ignores capital accumulation

and endogenous technical progress in order to focus on human resources mobilization, which has long

been a central concern of development theory (Lewis, 1954). Moreover, in our model, causality does not

go only from the expansion of market activities to the erosion of environmental (or social) assets but

also in the opposite direction, since the need to substitute for the services provided by declining

commons induces people to rely more heavily on market goods. Within this context, growth tends to go

‘too far’. Under laissez faire, indeed, the long-run equilibrium of the economy is characterized by: i) an

inefficiently high level of production, ii) an excessive portion of households’ time devoted to market

activities, and iii) an excessive depletion of the environmental (or social) asset. In addition, the model

shows that in an economy under laissez faire: iv) technological advances making labor more productive

increases the steady-state level of production, but they may lead to worsening the steady-state well-

being of the representative household; v) technological advances reducing the negative impact of

productive activities on the environmental (or social) asset decrease the steady-state level of production,

but they raise the steady-state well-being of the representative household; vi) technological advances

improving the ability of produced good to substitute for the environmental (or social) asset increase the

steady-state level of production, but they may worsen the steady-state well-being of the representative

household; vii) increases in population raise the steady-state level of per-capita, but they worsen the

steady-state well-being of the representative household.

Furthermore, the model studies the possible role that a regulatory authority can play in this

context. In principle, indeed, a regulatory authority can set a price for the use of the environmental (or

social) asset by the productive units so that the market economy can follow the Pareto-optimal path. In

this regulated economy, we have computed the ‘green’ net national product, that is an acceptable

approximation of the true human well-being at a given point in time, since it takes into account the value

of all components entering the individual utility function (inclusive of leisure time and of non-market

17

commodities such as those services rendered by environmental and social assets) and the value of the net

investment in environmental (or social) assets (see Asheim, 2000; Dasgupta and Mäler, 2000;

Weitzman, 2000). It is worth to emphasize that an important effect of this ‘green’ policy is to lead in the

long run to a reduction (relatively to the laissez-faire scenario) of the time devoted to market activities.

The model’s prediction according to which technological advances making labor more

productive in the market sector of the economy lead in the long run to an increase in labor supply and in

the level of market production may shed light on the reasons why technological progress does not bring

about marked reductions in labor time. As a matter of fact, even superficial examination of the evidence

breeds the suspicion that the long-run tendency for per-capita labor input to decline in response to

spectacular advances in labor productivity (GDP per hour worked) is relatively weak, displaying striking

reversals of tendency, and for long periods. For instance, the average weekly hours of market work per

person in the U.S. has been roughly constant since the 1950s.12 The explanation suggested by our model

of the tendency of labor supply to remain high in the presence of long-period productivity increases

relies on the fact that technological progress can accelerate the degradation of environmental and social

assets, by making more convenient to undertake market activities that erode these assets. This

explanation can be considered complementary to those explanations based on the concepts of

“preference for status”13 (see Cole et al., 1992; Fershtman et al., 1996; Corneo and Jeanne, 1999) and

12 According to the figures presented by Schor (1992), in 1987 Americans worked around one month per year more

than they did in 1969 (+163 hours). Obviously, satisfactory assessment of the extent to which total working time reacts

to productivity improvements also requires analysis of how productivity changes affect homework. This is especially

true in the light of the historical trend toward increased female labor-market participation distinctive of the advanced

countries during the twentieth century. However, the fact that the production of certain services is no longer confined to

the family is part of the general and progressive weakening of communitarian modes of life that has accompanied

modern economic growth.

13 “Preference for status” amounts to a concern for social status that may induce people to work and to save more than

they would have done if they did not care about their relative position in society with respect to income or wealth.

18

“conspicuous consumption”14 (see Veblen, 1967; Duesenberry, 1949), or on the idea that preferences are

manipulated by advertising through the media (see Benhabib and Bisin, 2002). It is apparent, however,

that these explanations have very different implications for social theory and economic policy.

APPENDIX Existence, uniqueness and local stability of H* Note the following three facts:

(i) H

Z)(H,

0;

(ii)

Z)(H,lim0H

;

(iii) 0A)-1(J=Z)(H,lim 1H

.

These three facts together ensures the existence of a unique steady-state value of H, H=H*. By inspecting (26), one can verify that tas *HH t if and only if

(iv) 1-H*)(J

-1

*HH1+t

1+t

1t

H

)(H

d

dR 1.

One can check that (iv) holds if and only if

(v) *HHH

Z)(H,

0,

which follows straightforwardly from (i).

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